A large fraction of engineered and natural systems are analyzed using scientific simulation codes that involve numerical solutions of partial differential equations (PDE). The Finite Element Method (FEM) is a widely popular approach for the numerical solution of PDEs in complex domains, with multiple $ billions/year spent in CAD and CAM (computer-aided design and manufacturing) based FEM software alone [1]}. The popularity arises from a compelling set of properties, including the ability (a) to model arbitrary geometries, (b) to change the order of representation (linear, quadratic, and higher-order), (c) to utilize variational arguments that guarantee monotonic convergence to the solution with improved discretization, and (d) to seamlessly utilize a posteriori error estimates to adapt the mesh. Over the past several years, we have developed a scalable FEM solver based on adaptive octree mesh and deployed this framework for a diverse array of multi-physics simulations–primarily on HPC resources [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}.
